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Description

Theoretical Mechanics for Sixth Forms, Volume 2 deals with mathematics as a double subject for sixth-form pupils. This book is a continuation of the revised edition of the course in Theoretical Mechanics.This volume discusses the principle of virtual work, stability of equilibrium, vector algebra, and the motion of bodies with variable mass—subjects that can help the student prepare for the freshman year in a university or in one of the polytechnic schools. Compared to the earlier edition, this volume discusses in more detail topics such as the motion of a particle in two dimensions and systems of coplanar forces. This book also emphasizes vector algebra and its many applications, explaining the concept of a vector, the Cartesian coordinates and components, the definitions of vectors and scalars, and vector applications to kinetics. This text also contains exercise problems with answers.This volume can be used for sixth-form students in the U.K. and is also suitable for third year students of a sixth form course as preparation for further studies.

Table of Contents

Preface
Chapter XV. The Motion of a Rigid Body about a Fixed Axis
15.1. The Definition of a Rigid Body
15.2. The Kinetic Energy of a Rigid Body Rotating about a Fixed Axis
15.3. Calculation of Moments of Inertia in Particular Cases
15.4. Conservation of Energy
15.5. The Compound Pendulum
15.6. The Equation of Motion for a Rigid Body Rotating about a Fixed Axis
15.7. The Force Exerted on the Axis of Rotation
15.8. Impulse and Momentum
15.9. Note on the Relationship between the Equations of Motion of Rotation of a Rigid Body and the Equations of Motion for a Particle Moving in a Straight Line
Chapter XVI. Free Motion of a Rum Body in Two Dimensions
16.1. Angular Velocity and Angular Acceleration
16.2. Instantaneous Center of Rotation
16.3. The Motion of a Rigid Lamina Referred to Its Center of Mass
16.4. The Kinetic Energy of a Lamina Moving in Its Plane
16.5. The Angular Momentum about an Arbitrary Axis Perpendicular to Its Plane of a Lamina Moving in Its Own Plane
16.6. Three-dimensional Motion
16.7. Impulsive Motion
16.8. Application to Problems
Chapter XVII. Motion with Variable Acceleration
17.1. Kinematics
17.2. Dynamical Problems
17.3. Rate of Working by a Variable Force
17.4. Equations of Motion Deduced from the Energy Equation
17.5. Damped Harmonic Oscillations
Chapter XVIII. Motion of a Particle in Two Dimensions
18.1. A Note on Vectors
18.2. Motion of a Particle in Two Dimensions—special Representations
18.3. Motion of a Particle on a Smooth Curve
18.4. The Angular Momentum of a Particle about an Axis
18.5. The Motion of a Projectile
Chapter XIX. Systems of Coplanar Forces
19.1. Forces Acting on a Particle
19.2. Coplanar Forces Acting on a Rigid Body
19.3. The Equivalence of Sets of Coplanar Forces
19.4. The Equilibrium of a Rigid Body under the Action of a System of Coplanar Forces
19.5. A Law of Vector Addition
19.6. The Moment of a Force as a Vector
Chapter XX. The Equilibrium of Rigid Bodies
20.1. Conditions of Equilibrium
20.2. Hinged Bodies
20.3. Problems of Equilibrium Involving More than One Body
20.4. The Equilibrium of the Hinge
Chapter XXI. The Principle of Virtual Work
21.1. The Work Done by a Force Acting on a Particle
21.2. The Potential Energy of a Particle
21.3. Extension to Rigid Bodies
21.4. The Principle of Virtual Work
21.5. Applications of the Principle of Virtual Work
Chapter XXII. Stability of Equilibrium
22.1. The Concept of Stability
22.2. Stability of Equilibrium
22.3. Rolling Stability - The Rocking Stone
Chapter XXIII. Light Frameworks
23.1. Graphical Method of Obtaining the Resultant of a System of Coplanar Forces
23.2. Light Frameworks
23.3. Calculation of the Stresses in the Bars of a Light Framework
23.4. Graphical Investigation of the Stresses in a Light Framework
23.5. The Method of Sections
Chapter XXIV. Continuously Distributed Forces
24.1. Introduction - Shearing Force and Bending Moment
24.2. Relations between Bending Moment, Shearing Force and Loading
24.3. A Uniform Flexible Inelastic String Hanging under Gravity
24.4. The Tightly Stretched Wire
24.5. A Uniformly Loaded Inextensible String
Chapter XXV. The Motion of Bodies with Variable Mass
25.1. Introduction
25.2. Rectilinear Motion of a Particle of Varying Mass—rockets
25.3. The Rectilinear Motion of Chains
Chapter XXVI. Vector Algebra
26.1. The Concept of a Vector
26.2. Cartesian Coordinates and Components
26.3. The Formula of Three-dimensional Coordinate Geometry
26.4. The Definitions of Vectors and Scalars
26.5. The Addition and Subtraction of Vectors
26.6. Some Applications of Vectors to Geometry
26.7. The Scalar Product
26.8. The Vector Product
26.9. Triple Products
26.10. Applications to Kinematics
Answers to the Exercises
Index